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Simplifying 15x2 + 92x = 60 Reorder the terms: 92x + 15x2 = 60 Solving 92x + 15x2 = 60 Solving for variable 'x'. Reorder the terms: -60 + 92x + 15x2 = 60 + -60 Combine like terms: 60 + -60 = 0 -60 + 92x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -4 + 6.133333333x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 6.133333333x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 6.133333333x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 6.133333333x + x2 = 0 + 4 6.133333333x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 6.133333333x + x2 = 4 The x term is 6.133333333x. Take half its coefficient (3.066666667). Square it (9.404444446) and add it to both sides. Add '9.404444446' to each side of the equation. 6.133333333x + 9.404444446 + x2 = 4 + 9.404444446 Reorder the terms: 9.404444446 + 6.133333333x + x2 = 4 + 9.404444446 Combine like terms: 4 + 9.404444446 = 13.404444446 9.404444446 + 6.133333333x + x2 = 13.404444446 Factor a perfect square on the left side: (x + 3.066666667)(x + 3.066666667) = 13.404444446 Calculate the square root of the right side: 3.661208058 Break this problem into two subproblems by setting (x + 3.066666667) equal to 3.661208058 and -3.661208058.Subproblem 1
x + 3.066666667 = 3.661208058 Simplifying x + 3.066666667 = 3.661208058 Reorder the terms: 3.066666667 + x = 3.661208058 Solving 3.066666667 + x = 3.661208058 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.066666667' to each side of the equation. 3.066666667 + -3.066666667 + x = 3.661208058 + -3.066666667 Combine like terms: 3.066666667 + -3.066666667 = 0.000000000 0.000000000 + x = 3.661208058 + -3.066666667 x = 3.661208058 + -3.066666667 Combine like terms: 3.661208058 + -3.066666667 = 0.594541391 x = 0.594541391 Simplifying x = 0.594541391Subproblem 2
x + 3.066666667 = -3.661208058 Simplifying x + 3.066666667 = -3.661208058 Reorder the terms: 3.066666667 + x = -3.661208058 Solving 3.066666667 + x = -3.661208058 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.066666667' to each side of the equation. 3.066666667 + -3.066666667 + x = -3.661208058 + -3.066666667 Combine like terms: 3.066666667 + -3.066666667 = 0.000000000 0.000000000 + x = -3.661208058 + -3.066666667 x = -3.661208058 + -3.066666667 Combine like terms: -3.661208058 + -3.066666667 = -6.727874725 x = -6.727874725 Simplifying x = -6.727874725Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.594541391, -6.727874725}
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